Global mechanical stop

ABSTRACT

Microstructure apparatus and methods are described. An exemplary movable microstructure apparatus includes a base, a plate, and a stop. The plate may be coupled to the base through a flexure, so that the plate is movable between a first angular orientation and a second angular orientation. The stop may be configured to contact the bottom portion of the plate in a contact area when the plate is in the second angular orientation. Alternatively, the stop may be configured to contact the plate in a contact area sized so that upon application of an electrostatic bias between the plate and the stop, a sufficient force holds the plate against the stop. Alternatively, the stop may have a substantially planar surface configured to contact the plate in a contact area sized so that, upon application of a force to the plate substantially normal to the substantially planar surface of the stop, a sufficient force holds the plate against the stop such that the plate lies in a plane substantially parallel to the substantially planar surface of the stop.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of prior U.S. ProvisionalApplication Ser. No. 60/123,496, filed Mar. 9, 1999.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

This invention was made with Government support under Grant No. DABT63-95-C-0055, which was awarded by the Defense Advanced ResearchProjects Agency (DARPA). The Government has certain rights in thisinvention.

BACKGROUND OF THE INVENTION

The present invention relates to movable microstructure methods andapparatus. Movable microstructures may be used in many differentapplications. For example, certain movable microstructures may be usedto implement large-port-count optical crossbar switches which facilitatethe flow of data over a computer network (e.g., the Internet).

The explosive growth of internet traffic in the last few years, and itsunabated continuation into the foreseeable future, has created anunprecedented demand on the communication infrastructure of both longdistance and interchange carriers. The term “fiber exhaust” was coinedin the last few years to describe the saturation of traffic in thepresent installed base of optical fibers. Thus ushered in the era ofwavelength division multiplex (WDM), a technique for using multiplecolors of light inside a single strand of fiber in order to boost thecapacity of the fiber manifold without actually having to install anynew fibers. But as internet traffic continues to grow, the fiber-opticnetwork infrastructure is encountering another bottleneck which WDM orsimilar solutions cannot solve. Interconnection between the growingnumber of channels supported by WDM systems demands solutions based onoptical-cross-connects (OXCs). Large-port-count optical crossbarswitches promise to be key components for performing OXC functions.

An optical crossbar switch can provide interchange of data paths betweendifferent fibers, at multi-gigabit data rates, without having to firstconvert them into the electronic domain as is being done in existingnetworks. An N×N optical crossbar switch consists of N input and Noutput optical fiber ports, with the capability of selectively directinglight from any input port to any output port in a “non-blocking”fashion. Currently, switches deployed in the communicationinfrastructure operate by converting the input optical signals toelectronic signals, directing the electronic signals to the properoutput channels, and converting them back into optical signals. In anall-optical OXC, the light is directly deflected from an input fiberport into an output fiber port without any electrical conversion. Eachof the optical beams can be expanded and collimated by inserting amicrolens at the tip of each input and output fiber port. By propagatingan array of optical beams in free space and selectively actuatingreflectors in an array of movable reflectors, any one of the N inputoptical beams can be directed to any one of the N output fibers ports.The core of each input and output fiber port is the region in which mostof the optical et beam travels. Due to the small diameter of the core,the optical crossbar switch requires the reflectors to be maintained ata precise position in order to direct each optical beam from one fiberport to another.

The optical crossbar switch has several inherent advantages over itselectronic counterpart, including data rate, format, wavelengthindependence, and lower costs. Furthermore, with advances inmicroelectromechanical systems (MEMS) technology, batch-processing andassembly methods similar to those used in the IC industry can beemployed to produce optical crossbar switches with high port-counts atvery low costs.

SUMMARY OF THE INVENTION

In one aspect, the invention features a movable microstructure apparatuscomprising a base, a plate having a bottom portion coupled to the baseso that the plate is movable between a first angular orientation and asecond angular orientation, and a stop configured to contact the bottomportion of the plate in a contact area when the plate is in the secondangular orientation.

In another aspect, the invention features a movable microstructureapparatus comprising a base, a plate coupled to the base and movablebetween a first angular orientation and a second angular orientation,and a stop configured to contact the plate in a contact area sized sothat, upon application of an electrostatic bias between the plate andthe stop, a sufficient force holds the plate against the stop.

Embodiments may include one or more of the following features.

The plate can be coupled to the base at an anchor location. The platecan be coupled to the base through a flexure. The flexure may be formedfrom a flexible and resilient material accommodating changes in theangular orientation of the plate about the anchor location with respectto the first angular orientation, and a lateral position of the platewith respect to the anchor location. The plate and the stop may eachcomprise a respective electrically conductive portion. The flexure maybe electrically conductive such that the plate can be set to ground or avoltage potential. Upon application of a magnetic field, the plate maymove to the second angular orientation and contact the stop in a contactarea characterized by a height b and width w that effectively satisfiesthe following condition: $\begin{matrix}{{\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{{b2} + {2{ab}}}{2}} \geq {k_{\theta}\theta}} & (1)\end{matrix}$where ε is a constant representing the permittivity of a materialseparating the electrically conductive portion of the plate and theelectrically conductive portion of the stop when the plate is in contactwith the stop, V is a voltage applied to create an electrostatic biasbetween the plate and the stop, g is a distance separating theelectrically conductive portion of the plate and the electricallyconductive portion of the stop when the plate is in contact with thestop, k_(θ) is a torsional spring constant of the flexure, θ is theangular orientation of the plate about the anchor location with respectto the first angular orientation, and a is a distance separating thestop and the base. If the second angular orientation is an obtuse angleabout the anchor location with respect to the first angular orientation,the plate may move to the second angular orientation and contact thestop in a contact area characterized by a height b and a width wprovided two conditions are satisfied: (i) condition 1 defined above;and (ii) the following condition: $\begin{matrix}{{\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{b^{2}}{2}} \geq {{kd}\left( {a + b} \right)}} & (2)\end{matrix}$where k is a lateral spring constant of the flexure, and d is a distanceseparating the anchor location and a plane defined by the contact areaof the stop. Alternatively, if the second angular orientation is anacute angle about the anchor location with respect to the first angularorientation, the plate may move to the second angular orientation andcontact the stop in a contact area characterized by a height b and awidth w provided two conditions are satisfied: (i) condition 1 definedabove; and (ii) the following condition: $\begin{matrix}\left. {{\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{b^{2}}{2}} \geq {kda}} \right) & (3)\end{matrix}$where k is a lateral spring constant of the flexure, and d is a distanceseparating the anchor location and a plane defined by the contact areaof the stop.

The flexure may be formed from polycrystalline-silicon and may includebut not be limited to torsional, serpentine, cantilever, and combinationof pin-and-staple rotational hinges and/or hinges and flexures havinglateral compliance. The flexure may pull the plate from a second angularorientation to a first angular orientation when the electrostatic forcecoupling the stop and plate is released. The contact area may comprise asubstantially planar surface configured to define a lateral position ofthe plate with respect to an anchor location and the second angularorientation of the plate about the anchor location with respect to thefirst angular orientation when a force is applied between the plate andthe stop. The contact area may also generally comprise the overlap areaof the plate and the stop where textured surfaces are used to preventsticking effects of substantially planar surfaces. The substantiallyplanar contact area surface may be substantially perpendicular to a topsurface of the base. The force may be an electrostatic force. The base,the plate and the stop may be formed from a semiconductor material. Theplate may have a current-carrying coil, a hard magnetic material, a softmagnetic material, or a combination of the three. The plate may have alight-reflecting surface. The plate may be one of an array of platescoupled to the base, each plate having a respective stop configured tocontact the plate in a contact area. The respective stops may be formedfrom or be part of a single global mechanical stop array.

In another aspect, the invention features a movable microstructureapparatus comprising a base, a plate coupled to the base and movablebetween a first position and a second position, and a stop having asubstantially planar surface configured to contact the plate in acontact area sized so that, upon application of a force to the platesubstantially normal to the substantially planar surface of the stop, asufficient force holds the plate against the stop such that the platelies in a plane substantially parallel to the substantially planarsurface of the stop.

In yet another aspect, the invention features a method for directing anoptical beam from a first port to a second port. The method comprisesapplying a first force to a plate to move the plate from a first angularorientation to a second angular orientation, wherein the plate contactsa stop in the second angular orientation, and applying a second forcebetween the plate and the stop to hold the plate against the stop in aplane substantially parallel to a substantially planar surface of thestop, such that the plate directs an optical beam from a first port to asecond port. The first force may be a magnetic field; the second forcemay be an electrostatic bias.

In yet another aspect, the invention features a method for directing anoptical beam from a first port to a second port using a light-reflectiveplate having a first angular orientation in the absence of an appliedforce and a static equilibrium position in the presence of a steadyforce. The method comprises applying a first force to the plate to movethe plate from the first angular orientation to a second angularorientation other than the static equilibrium position, wherein theplate contacts a stop in the second angular orientation, and applying asecond force between the plate and the stop to hold the plate againstthe stop in a plane substantially parallel to a substantially planarsurface of the stop, such that the plate directs an optical beam from afirst port to a second port.

Embodiments may include one or more of the following features.

The first force may be a time-varying force. The first force may have aprofile selected from a group consisting of a step profile, a rampprofile, a sinusoidal profile, and a pulse profile. The first force maybe a magnetic field. The second force may be an electrostatic bias.

In yet another aspect, the invention features a method for manufacturingan apparatus for directing optical beams. The method comprises couplingan array of plates to a base assembly, each plate being movable betweena first angular orientation and a second angular orientation, andforming an array of apertures in a stop assembly, the stop assemblybeing coupled to the base assembly, and each aperture being positionedto contact its respective plate when the plate is in the second angularorientation.

Embodiments may include one or more of the following features.

Each aperture may be constructed to have at least one substantiallyplanar sidewall constructed to lie in a plane orthogonal to a topsurface of the base assembly. Each plate may be coupled to the baseassembly through at least one flexure.

Advantages that can be seen in implementations of the invention includeone or more of the following. The invention can produce an opticalcrossbar switch having very low insertion loss. The precise positioningof the reflectors enabled by the invention can be used in applicationsthat integrate micro-optical elements, for example, lasers, lenses,movable reflectors and beam splitters, on a silicon chip.

The details of one or more embodiments of the invention are set forth inthe accompanying drawings and the description below. Other features andadvantages of the invention will become apparent from the followingdescription, including the drawings and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic perspective view of a movable microstructureapparatus.

FIG. 2 a is a diagrammatic top view of a movable microstructureapparatus having a different lateral position with respect to an anchorlocation and a different angular orientation about an anchor locationwith respect to a first angular orientation.

FIG. 2 b is a diagrammatic side view of a movable microstructureapparatus having a different lateral position with respect to an anchorlocation and a different angular orientation about an anchor locationwith respect to a first angular orientation.

FIGS. 3 a-3 f are diagrammatic perspective views of the movablemicrostructure apparatus of FIG. 1 upon application of variouscombinations of a magnetic field and an electrostatic bias.

FIG. 4 a is a diagrammatic side view of a movable microstructureapparatus, where a base and a stop have a slight misalignment.

FIG. 4 b is a diagrammatic side view of the movable microstructureapparatus of FIG. 4 a upon application of a magnetic field.

FIG. 4 c is a diagrammatic side view of the movable microstructureapparatus of FIG. 4 a upon application of an electrostatic bias betweenthe plate and the stop.

FIG. 4 d is a diagrammatic front view of the movable microstructureapparatus of FIG. 4 c.

FIG. 5 a is a diagrammatic side view of a movable microstructureapparatus, where a base and a stop have a slight misalignment.

FIG. 5 b is a diagrammatic side view of the movable microstructureapparatus of FIG. 5 a upon application of a magnetic field.

FIG. 5 c is a diagrammatic side view of the movable microstructureapparatus of FIG. 5 a upon application of an electrostatic bias betweenthe plate and the stop.

FIG. 6 a is a diagrammatic perspective view of an N×M system movablemicrostructure apparatus used as an optical switch.

FIG. 6 b is a diagrammatic top view of the N×M system movablemicrostructure apparatus of FIG. 6 a.

FIG. 7 a is a diagrammatic side view of the movable microstructureapparatus of FIG. 1 upon application of a magnetic field, where themagnetic field is not parallel to a sidewall of a stop.

FIG. 7 b is a diagrammatic front view of an alternate embodiment of amovable microstructure apparatus.

FIG. 7 c is a diagrammatic side view of the movable microstructureapparatus of FIG. 7 b upon application of a magnetic field, where themagnetic field is not parallel to a sidewall of a stop.

DETAILED DESCRIPTION

FIG. 1 shows an apparatus 100 having a stop 102, a base 104 and a plate106. The plate 106 is coupled to the base 104 and is movable between afirst angular orientation and a second angular orientation. The stop 102has at least one substantially planar sidewall 108 that is configured tocontact the plate 106 in a contact area when the plate 106 is in thesecond angular orientation. In one implementation, a substantiallyplanar sidewall 108 is constructed to lie in a plane which is orthogonalto the top surface of the base 104.

The apparatus 100 is fabricated by a MEMS process. The base 104 may becomposed of an insulating layer disposed over a semiconductor substrate;for example, silicon nitride, silicon oxide, or a combination of both,may be disposed over a silicon substrate. The plate 106 may be arectangular beam formed from a conductive material or a semiconductivematerial such as polycrystalline silicon. A layer of magnetic materialmay be plated onto the plate 106. More than one region of the plate 106may be so plated. The magnetic material may be one of variouscombinations of nickel, iron, or other elements, and is usuallyferromagnetic characterized by a high saturation magnetization.

The plate 106 may be coupled through flexures 110 and 112 to the base104 at anchor locations. In one implementation, insulative anchors 114and 116 are used to attach the flexures 110 and 112 to the base 104. Theflexures 110 and 112 may be formed from a flexible and resilientconductive or semiconductive material (e.g., polycrystalline silicon).The flexible material provides the flexures 110 and 112 with a degree ofelasticity. The flexures 110 and 112 allow the plate 106 to change itsangular orientation about the anchors 114 and 116 with respect to thefirst angular orientation and its lateral position with respect to theanchors 114 and 116, as shown in FIGS. 2 a and 2 b.

In one implementation, the stop 102 is coupled to a voltage source 118and the base 104 is electrically grounded. An electrostatic clampingcircuit can be formed from a switch 120, a contact 122 for forming aconnection between the switch 120 and the flexure 110, the plate 106,the flexure 112, and the anchor 116, and is switchable between a voltagesource 124 and electrical ground 126. The voltage sources 118 and 124may be external sources such as power supplies or batteries, or internalsources on the apparatus 100. An electrostatic bias can be createdbetween the plate 106 and one of the clamping surfaces (base 104 andstop 102) depending on the position of the switch 120.

Referring to FIG. 3 a, in the absence of any applied force, the plate106 lies in the first angular orientation substantially parallel to thebase 104. The voltage source 124 may be coupled to the electrostaticclamping circuit to create an electrostatic bias between the plate 106and the base 104 upon application of a voltage V1. If a sufficientvoltage V1 is applied, the plate 106 is “clamped” to the base 104 andrestrains the plate 106 from rotating in the presence of an appliedforce, for example, a magnetic field 126 as shown in FIG. 3 b. If theplate 106 is not clamped to the base 104, application of the magneticfield 126 would cause the plate 106 to be rotated about the anchors 114and 116 between the first angular orientation and the second angularorientation until there is an equilibrium between the resultant torquefrom the torsional stretching of the flexures 110 and 112 and the forceon the plate 106 caused by the magnetic field 126. The angularorientation of the plate 106 at the equilibrium point defines a staticequilibrium position. In one implementation, the static equilibriumposition is the second angular orientation, as shown in FIG. 3 c. Inanother implementation, the static equilibrium position is between thefirst angular orientation and the second angular orientation, as shownin FIG. 3 d. In this implementation, the force on the plate 106resulting from the application of the magnetic field 126 can betime-varying, such that the plate 106 is provided with a momentum thatrotates the plate 106 beyond the static equilibrium position to thesecond angular orientation. The time-varying force on the plate 106 mayhave a step profile, a ramp profile, a sinusoidal profile or a pulseprofile. Once the plate 106 is in the second angular orientation, anelectrostatic bias may be created between the plate 106 at electricalground and the stop 102 having a voltage V2, as shown in FIG. 3 e. Theplate 106 clamps to the sidewall 108 in a contact area characterized bya height b and a width w provided the following condition is satisfied:$\begin{matrix}{{\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{{b2} + {2{ab}}}{2}} \geq {k_{\theta}\theta}} & (1)\end{matrix}$where ε is a constant representing the permittivity of a materialseparating the electrically conductive portion of the plate 106 and theelectrically conductive portion of the stop 102 when the plate 106 is incontact with the stop 102, V is a voltage applied to create anelectrostatic bias between the plate 106 and the stop 102, g is adistance separating the electrically conductive portion of the plate 106and the electrically conductive portion of the stop 102 when the plate106 is in contact with the stop 102, k_(θ) is a torsional springconstant of the flexures 110 and 112, θ is the angular orientation ofthe plate 106 about the anchors 114 and 116 with respect to the firstangular orientation, and a is a distance separating the stop 102 and thebase 104. Once the plate 106 is clamped to the sidewall 108, removingthe magnetic field 126 has no effect on the angular orientation of theplate 106, as shown in FIG. 3 f.

FIG. 4 a shows the stop 102 coupled to the base 104 with a slightmisalignment. In this example, the anchors 114 and 116 are offset from aplane 402 defined through the contact area of stop 102. The plate 106 ismovable through an obtuse angle e about the anchors 114 and 116 withrespect to the first angular orientation. In the absence of an appliedforce, the plate 106 lies in the first angular orientation substantiallyparallel to the base 102. If the plate 106 is not clamped to the base104, application of the magnetic field 126 may rotate the plate 106about the anchors 114 and 116 until the plate 106 contacts a top edge128 of the stop 102 in the second angular orientation, as shown in FIG.4 b. The plate 106 clamps to the sidewall 108 in a contact areacharacterized by a height b and a width was shown in FIGS. 4 c and 4 dprovided two conditions are satisfied: (i) condition 1 defined above;and (ii) the following condition: $\begin{matrix}\begin{matrix}{{torque}\quad{about}\quad{axis}\quad{defined}\quad{through}\quad{top}} & {{{torque}\quad{resulting}\quad{from}}\quad} \\{{{edge}\quad 128\quad{resulting}\quad{from}\quad{electrostatic}\quad{bias}} \geq} & {{the}\quad{lateral}\quad{stretching}\quad{of}} \\{{created}\quad{between}\quad{plate}\quad 106\quad{and}\quad{stop}\quad 102} & {{flexures}\quad 110\quad{and}\quad 112}\end{matrix} & \quad \\{{\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{b^{2}}{2}} \geq {{kd}\left( {a + b} \right)}} & (2)\end{matrix}$where k is a lateral spring constant of the flexures 110 and 112, and dis a distance separating the location of the anchors 114 and 116 and aplane defined by the contact or overlap area 404 of the stop 102.

FIG. 5 a shows the stop 102 coupled to the base 104 with an alternativemisalignment. In this example, the anchors 114 and 116 are offset from aplane 502 defined through the contact area of the stop 102. The plate106 is movable through an acute angle θ about the anchors 114 and 116with respect to the first angular orientation. In the absence of anapplied force, the plate 106 lies in the first angular orientationsubstantially parallel to the base 102. If the plate 106 is not clampedto the base 104, application of the magnetic field 126 may rotate theplate 106 about the anchors 114 and 116 until the plate 106 contacts abottom edge 130 of the stop 102 in the second angular orientation, asshown in FIG. 5 b. The plate 106 clamps to the sidewall 108 in a contactarea characterized by a height b and a width w as shown in FIG. 5 cprovided two conditions are satisfied: (i) condition 1 defined above;and (ii) the following condition: $\begin{matrix}\begin{matrix}{{torque}\quad{about}\quad{axis}\quad{defined}\quad{through}\quad{bottom}} & {{{torque}\quad{resulting}\quad{from}}\quad} \\{{{edge}\quad 130\quad{resulting}\quad{from}\quad{electrostatic}\quad{bias}} \geq} & {{the}\quad{lateral}\quad{stretching}\quad{of}} \\{{created}\quad{between}\quad{plate}\quad 106\quad{and}\quad{stop}\quad 102} & {{flexures}\quad 110\quad{and}\quad 112}\end{matrix} & \quad \\{{\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{b^{2}}{2}} \geq {kda}} & (3)\end{matrix}$

In the three cases described above and shown in FIGS. 3 f, 4 c and 5 c,in the absence of an applied force, the plate 106 returns to the firstangular orientation substantially parallel to the base 104 as thetorsional and lateral stretching of the flexures 110 and 112 arerelaxed.

FIGS. 6 a and 6 b show an apparatus 600 having a stop assembly 602coupled to a base assembly 604. The base assembly 604 has an array ofplates 606. Each plate is coupled to the base assembly 604 by at leastone flexure which permits each plate to change its angular orientationand lateral position. The stop assembly 602 may have an array ofsubstantially planar surfaces. Each substantially planar surface may beconfigured to contact a respective plate in a contact area sized sothat, upon application of a force to the plate substantially normal tothe substantially planar surface of the stop assembly 602, a sufficientforce holds the plate against the stop assembly 602 in a planesubstantially parallel to the substantially planar surface of the stopassembly 602. In one implementation, the stop assembly 602 defines anarray of apertures 608, as shown in FIG. 6 a. Each aperture has at leastone substantially planar surface 610 that contacts a respective plate ina contact area. Each substantially planar surface 610 is constructed tolie in a plane normal to the base assembly 604. The array of plates 606may be coupled to an electrostatic clamping circuit such that each platemay be individually selected to be clamped to its respective surface 610or to the base assembly 604. In an alternative implementation (notshown), the stop assembly may define an array of cavities, each cavityhaving at least one substantially planar surface that contacts arespective plate in a contact area.

One application of the apparatus 600 is an optical switch. In oneimplementation, the array of plates 606 act as reflectors. A suitablereflector coating may be deposited on the portion of each plate abovethe plane of a top surface 612 of the stop assembly 602 to enhancereflectivity if desired. In an alternative implementation, the array ofplates 606 act as beam splitters. Each plate may be constructed from amaterial that transmits and reflects different parts of an optical beam.Each plate may be similarly sized and constructed such that eachsidewall 610 contacts a bottom portion of its respective plate.

FIG. 6 a shows the apparatus 600 having three optical inputs 614, 616and 618, and three optical outputs 620, 622 and 624. The N inputs (614,616 and 618) are along one side of the apparatus 600 and the M outputs(620, 622 and 624) are along an adjacent side. The switching elementsare the array of plates 606. Each plate is oriented at a similar angle,for example, 45 degrees to an incoming optical beam. If the mth platealong one of the N input beams is clamped to its respective sidewall,that beam is reflected into the mth of the M outputs. All but one platein a given input line may be held down by the electrostatic bias appliedbetween the plate and the base assembly 604. The plate that is clampedto its respective sidewall selects the output for that input line.

The materials from which the apparatus 600 is fabricated, the voltagesources, the applied electrostatic bias, and the applied magnetic fieldsmay be chosen by a user to adjust the sensitivity of the apparatus 600for any particular purpose or application. The apparatus 600 may befabricated using techniques including “lithographic, galvanoformung andabformung” (LIGA), traditional machining, deep anisotropic plasmaetching and laser machining. The stop assembly 602 may be fabricated byanisotropic etching of (110)-oriented silicon which ensures the angularuniformity of all the sidewalls 610 on the stop assembly 602. The arrayof plates 606, sidewalls 610 and the base assembly 604 may be fabricatedto have textured surfaces on one or more surfaces to reduce stickingwhen a plate is clamped to its respective sidewall or to the baseassembly 604. The textured surface may include dimples, bumps, andridges such that the contact area may include the overlap area betweenthe plate and the stop at a distance gap generally equal to theeffective height of the texture. The number of plates defining theN-by-M array of plates 606 may be adjusted based on the application ofthe apparatus 600. The apparatus 600 may be fabricated in a singlebatch-process and consist of a single stop-base module. Alternatively,the apparatus 600 may be fabricated in a two-part process, one processfor fabricating the stop assembly 602 and the other process forfabricating the base assembly 604. The stop assembly 602 may be alignedwith the base assembly 604 in a separate alignment step.

The applied electrostatic bias may be an attractive force applied by theelectrostatic clamping circuit described above or by other means, wherethe attractive force is defined as any force that pushes or pulls aplate towards a stop.

The magnetic fields may be applied using coils located internal orexternal to the apparatus 600, or a permanent magnet located internal orexternal to the apparatus 600. Current-carrying coils, hard magneticmaterials, soft magnetic materials, or a combination of the three formedon each of the array of plates 606 may apply a force to the plate in thepresence of magnetic fields. An applied magnetic field 702 that is notperfectly parallel to the sidewall 704 may induce a slight torque andresultant bending in the portion of the plate 706 containing areflective surface when the plate 706 is clamped to the sidewall 704, asshown in FIG. 7 a. The resultant bending may cause a misalignment of areflected beam. FIG. 7 b shows an alternative implementation to theplate 706 that reduces the bending effects on optical performance. Themagnetic portion 708 of the plate 710 is connected to the rest of theplate 710 by support arms 712. The support arms 712 isolate the portionof the plate 710 containing a reflective surface 714 from the magneticfield 702 that is applied on the magnetic portion 708 of the plate 710.In this implementation, when the plate 710 is clamped to the sidewall716, application of the magnetic field 702 that is not perfectlyparallel to the sidewall 716 results in minimal bending in the portionof the plate 710 containing the reflective surface 714 as shown in FIG.7 c.

The invention has been described in terms of particular embodiments.Other embodiments are within the scope of the following claims. Forexample, the steps of the invention can be performed in a differentorder and still achieve desireable results.

1. An apparatus, comprising: a base; a plate having a bottom portioncoupled to a top surface of the base so that the plate is movablebetween a first angular orientation adjacent to the top surface of thebase and a second angular orientation away from the base; and a stoppositioned above the top surface of the base, the stop has an apertureand a portion of a sidewall of the aperture contacts the plate in acontact area when the plate is in the second angular orientation and thestop is further configured to prevent the plate from rotating beyond thesecond angular orientation.
 2. An apparatus, comprising: a base; a platecoupled to a top surface of the base and movable between a first angularorientation adjacent to the top surface of the base and a second angularorientation away from the base; and a stop positioned above the topsurface of the base, wherein the stop has an aperture and a portion of asidewall of the aperture contacts the plate in a contact area sized sothat, upon application of an electrostatic bias between the plate andthe stop, a sufficient force holds the plate against the stop, the stoppreventing the plate from rotating beyond the second orientation.
 3. Theapparatus of claim 1 or 2, wherein the plate is coupled to the base atan anchor location.
 4. The apparatus of claim 3, wherein the plate iscoupled to the base through a flexure.
 5. The apparatus of claim 4,wherein the flexure is formed from a flexible and resilient materialaccommodating changes in: the angular orientation of the plate about theanchor location with respect to the first angular orientation; and alateral position of the plate with respect to the anchor location. 6.The apparatus of claim 5, wherein the plate and the stop each comprisesa respective electrically conductive portion.
 7. The apparatus of claim6, wherein: upon application of a magnetic field, the plate moves to thesecond angular orientation and contacts the stop in a contact areacharacterized by a height b and a width w that effectively satisfies thefollowing condition:${\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{b^{2} + {2{ab}}}{2}} \geq {k_{\theta}\theta}$where ε is a constant representing the permittivity of a materialseparating the electrically conductive portion of the plate and theelectrically conductive portion of the stop when the plate is in contactwith the stop, V is a voltage applied to create an electrostatic biasbetween the plate and the stop, g is a distance separating theelectrically conductive portion of the plate and the electricallyconductive portion of the stop when the plate is in contact with thestop, k_(θ) is a torsional spring constant of the flexure, θ is theangular orientation of the plate about the anchor location with respectto the first angular orientation, and a is a distance separating thestop and the base.
 8. The apparatus of claim 7, wherein the platecontacts the stop in a contact area characterized by a height b and awidth w that further satisfies the following condition when the secondangular orientation is an obtuse angle about the anchor location withrespect to the first angular orientation:${\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{b^{2}}{2}} \geq {{kd}\left( {a + b} \right)}$where k is a lateral spring constant of the flexure, and d is a distanceseparating the anchor location and a plane defined by the contact areaof the stop.
 9. The apparatus of claim 7, wherein the plate contacts thestop in a contact area characterized by a height b and a width w thatfurther satisfies the following condition when the second angularorientation is an acute angle about the anchor location with respect tothe first angular orientation:${\frac{ɛ\quad{wV}^{2}}{2g^{2}} \times \frac{b^{2}}{2}} \geq {kda}$where k is a lateral spring constant of the flexure, and d is a distanceseparating the anchor location and a plane defined by the contact areaof the stop.
 10. The apparatus of claim 5, wherein the flexure is formedfrom polycrystalline-silicon.
 11. The apparatus of claim 1, wherein thecontact area comprises a substantially planar surface configured todefine a lateral position of the plate with respect to an anchorlocation and the second angular orientation of the plate about theanchor location with respect to the first angular orientation when aforce is applied between the plate and the stop.
 12. The apparatus ofclaim 11, wherein the substantially planar surface of the contact areais substantially perpendicular to the top surface of the base.
 13. Theapparatus of claim 11, wherein the force is an electrostatic force. 14.The apparatus of claim 1 or 2, wherein the base, the plate and the stopare formed from a semiconductor material.
 15. The apparatus of claim 1or 2, wherein the plate comprises a current-carrying coil.
 16. Theapparatus of claim 1 or 2, wherein the plate comprises a hard magneticmaterial.
 17. The apparatus of claim 1 or 2, wherein the plate comprisesa soft magnetic material.
 18. The apparatus of claim 1 or 2, wherein theplate comprises a light-reflecting surface.
 19. The apparatus of claim 1or 2, wherein the plate is one of an array of plates coupled to thebase, each plate having a respective stop configured to contact theplate in a contact area.
 20. An apparatus comprising: a base; a platecoupled to a top surface of the base and movable between a firstposition adjacent to the top surface of the base and a second positionaway from the base; and a stop positioned above the top surface of thebase, the stop has an aperture and a substantially planar surface of asidewall of the aperture contacts of the plate in a contact area sizedso that, upon application of a force to the plate substantially normalto the substantially planar surface of the stop, a sufficient forceholds the plate against the stop such that the plate lies in a planesubstantially parallel to the substantially planar surface of the stopsuch that the stop prevents the plate from rotating beyond the secondposition.
 21. The apparatus of claim 20, wherein the plate is coupled tothe base at an anchor location.
 22. The apparatus of claim 21, whereinthe plate is coupled to the base through a flexure.
 23. The apparatus ofclaim 22, wherein the flexure is formed from a flexible and resilientmaterial accommodating changes in: an angular orientation of the plateabout the anchor location with respect to the first position; and alateral position of the plate with respect to the anchor location. 24.The apparatus of claim 23, wherein the flexure is formed frompolycrystalline-silicon.
 25. The apparatus of claim 20, wherein thesubstantially planar surface is substantially perpendicular to a topsurface of the base.
 26. The apparatus of claim 20, wherein the base,the plate and the stop are formed from a semiconductor material.
 27. Theapparatus of claim 20, wherein the plate comprises a current-carryingcoil.
 28. The apparatus of claim 20, wherein the plate comprises a hardmagnetic material.
 29. The apparatus of claim 20, wherein the platecomprises a soft magnetic material.
 30. The apparatus of claim 20,wherein the plate comprises a light-reflecting surface.
 31. Theapparatus of claim 20, wherein the plate is one of an array of platescoupled to the base, each plate having a respective aperture including asubstantially planar surface of a sidewall configured to contact theplate in a contact area.
 32. The apparatus of claim 4 wherein theflexure is electrically conductive.
 33. The apparatus of claim 32wherein the flexure enables the plate to return to the first angularorientation from the second angular orientation.
 34. The apparatus ofclaim 22 wherein the flexure is electrically conductive.
 35. Theapparatus of claim 34 wherein the flexure enables the plate to return tothe first position from the second position.
 36. The apparatus of claim1 or 2, wherein at least one of the plate, the base and the stop has atextured surface.
 37. An apparatus, comprising: a base; a plate having abottom portion coupled to a top surface the base so that the plate ismovable between a first angular orientation adjacent to the top surfaceof the base and a second angular orientation away from the base, theplate having a magnetic portion that is separate from a reflectivesurface of the plate to reduce any bending of the reflective surfacecaused by an applied magnetic field; and a stop positioned above the topsurface of the base, the stop has an aperture and a portion of asidewall of the aperture contacts the plate in a contact area when theplate is in the second angular orientation and the stop is furtherconfigured to stop the plate from rotating beyond the second angularorientation.
 38. The apparatus of claim 1, wherein: the stop isimmobile.
 39. The apparatus of claim 2, wherein: the stop is immobile.40. The apparatus of claim 20, wherein: the stop is immobile.
 41. Theapparatus of claim 37, wherein: the stop is immobile.
 42. The apparatusof claim 2, wherein: at least one of the stop is substantiallyperpendicular to the top surface of the base.
 43. The apparatus of claim37, wherein: at least one surface of the stop is substantiallyperpendicular to the top surface of the base.